Answer to Question #229223 in Chemical Engineering for Lokika

Question #229223

Solve dy/dx= 4x² (y-x)² + if y /x is a particular solution.


1
Expert's answer
2021-08-28T06:16:19-0400

Given DE:


"dy\/dx= 4x\u00b2 (y-x)\u00b2 +y\/x"

Let

"u(x)=y\/x"

Then

"y=u\\cdot x,\\quad y'=u'x+u"

We get

"u'x+u=4x^2(ux-x)^2+u""u'x=4x^4(u-1)^2"

"\\frac{du}{(u-1)^2}=4x^3dx"

"-\\frac{1}{u-1}=x^4+C"

"u-1=-\\frac{1}{x^4+C}"

"u=1-\\frac{1}{x^4+C}"

Finally

"y(x)=x\\left(1-\\frac{1}{x^4+C}\\right)"


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS